Re: additive 2-categories and related structures?

[Urs Schreiber <urs.schreiber@googlemail.com>]

Dear Ronnie,

only just saw your message via David's reply.

Just for completeness it seems one should say that there is quite a
bit known about additive n-categories even for n all the way from 1 to
infinity -- they are called stable infinity-categories. Examples of
these are in particular given by modules over infinity-rings -- which
are maybe better known as ring spectra!

A modern entry point into the theory, from a category-theoretic point of view is

Jacob Lurie
Commutative algebra
http://arxiv.org/abs/math/0703204

But the basic elements and examples of the theory, such as
E-infinity-rings, A-infinity-algebras and their modules and module
categories are of course way older and quite classical even.

All the best
Urs

On Mon, Aug 30, 2010 at 3:18 AM, David Roberts
<droberts@maths.adelaide.edu.au> wrote:
> Hi Ronnie,
>
> There is the work of Matthieu Dupont, see his page
>
> http://breckes.org/dom-en.html
>
> His PhD thesis is on abelian categories in dimension 2.
>
> David
>

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